Cone-beam computed tomography (CBCT) is a valuable imaging method in dental diagnostics that provides information not available in traditional 2D imaging. However, interpretation of CBCT images is a time-consuming process that requires a physician to work with complicated software. In this work we propose an automated pipeline composed of several deep convolutional neural networks and algorithmic heuristics. Our task is two-fold: a) find locations of each present tooth inside a 3D image volume, and b) detect several common tooth conditions in each tooth. The proposed system achieves 96.3\% accuracy in tooth localization and an average of 0.94 AUROC for 6 common tooth conditions.